Right Pyramids, Right Cones and Spheres (Grade 10 NSC Matric Mathematics): Flashcards

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Right Pyramids, Right Cones and Spheres
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Right pyramid definition

Pyramid with apex-to-base-centre line perpendicular to base

Apex in pyramids

Single point where triangular faces meet at top

Sphere definition

Round 3D shape, all surface points equidistant from centre

Height vs slant height difference

Height: perpendicular to base; Slant: diagonal along face

Sphere surface area formula

4πr24\pi r^2

Sphere volume formula

43πr3\frac{4}{3}\pi r^3

Right cone surface area formula

πr(r+h)\pi r(r + h)

Right cone volume formula

13×πr2×H\frac{1}{3} \times \pi r^2 \times H

Volume factor for pyramids and cones

One-third of base area times height

Slant height from height & radius (Pythagoras)

s2=H2+r2s^2 = H^2 + r^2

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